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Functions as Machines
Functions as Machines
Think of a function as a machine: you put a number in, it does something, and a different number comes out. An INVERSE function is a machine that UNDOES what the first machine did - it takes the output and gives you back the original input! It's like having an "undo" button for mathematics.
What is an inverse function?: A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)
Mathematics glossary
- What is an inverse function?
- A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)
Key Facts
Key insight: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x
Earn the mark scheme marks
Common Mistakes to Avoid
✗ Forgetting to swap x and y
✓ Always swap before rearranging
This is the crucial step that "undoes" the function
✗ Not verifying your answer
✓ Check that f(f⁻¹(x)) = x
Verification confirms you've done it correctly
✗ Confusing f⁻¹(x) with 1/f(x)
✓ f⁻¹ means inverse, not reciprocal
Inverse function ≠ reciprocal function
Now try it yourself
Quiz · Question 1 of 8
What does f⁻¹(x) represent?
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on inverse functions, with a full worked answer.
AQA Paper 2
Three of the four sittings we have full papers for require finding an inverse function, or combining a function with a composite or its inverse.
Edexcel Paper 1
Two of the three sittings we have full papers for build a question around inverse and composite functions together, one proving a quadratic equation and one solving for a specific value.